Since October 2013 a new devastating plant disease, known as Olive Quick Decline Syndrome (OQDS), spread in Apulia (Salento, Lecce district, South Italy), causing the infection of millions of olive trees distributed in more than 23000 ha of olive orchards). It has been ascertained [1] that the bacterium responsible for the OQDS outbreak in the olive groves of Apulia is the Xylella Fastidiosa and the principal vector [2] of this bacterium is the meadow spittlebug, Philaenus spumarius. We construct a model for the spreading of OQDS, in which the olive orchard is depicted as a simple square lattice with olive trees and herbaceous vegetation distributed on the lattice sites in a realistic way according to conventional plantation schemes of Italian olive orchards. We compare the efficiency of different kind of preventive measures: removal of the nymphal phase on spontaneous vegetation, chemical treatments acting against adult vectors, uprooting of infected olive trees, etc. It emerges that appropriate combinations of these treatments allow reducing the OQDS outbreak significantly.